Questions on Algebra: Distributive, associative, commutative properties, FOIL answered by real tutors!

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Question 1170955: IQ is normally distributed with a mean of 100 and a standard deviation of 15.
a) Suppose one individual is randomly chosen. Find the probability that this person has an IQ greater than 95.
Write your answer in percent form. Round to the nearest tenth of a percent.
P
P
(IQ greater than 95) = %
b) Suppose one individual is randomly chosen. Find the probability that this person has an IQ less than 125.
Write your answer in percent form. Round to the nearest tenth of a percent.
P
P
(IQ less than 125) = %
c) In a sample of 600 people, how many people would have an IQ less than 110?
people
d) In a sample of 600 people, how many people would have an IQ greater than 140?
people

Click here to see answer by CPhill(1959) About Me 

Question 1179597: Formulate a simple geometric statement that can be proven using
any combination of the following: congruence axioms, substitution, and
definitions. Show two different ways to prove this statement.

Click here to see answer by CPhill(1959) About Me 

Question 1179598: Write a proof for each of the following.
1. Given: 𝑚∠1 = 90°;∠1 ≅ ∠2
Prove: ∠2 is a right angle
2. Given: 3(x + 1) = 6(x - 3)
Prove: x = 7
3. Given: 𝑚∠1 = 180°;∠1 ≅ ∠2; 𝑚∠2 ≅ 𝑚∠3
Prove: ∠3 is a straight angle.
4. Given 8.5s - 81.7 = -9.23s + 148.79
Prove: s = 13

Click here to see answer by CPhill(1959) About Me 

Question 1179644: 1. Given: 𝑚∠1 = 90°;∠1 ≅ ∠2
Prove: ∠2 is a right angle
2. Given: 3(x + 1) = 6(x - 3)
Prove: x = 7
3. Given: 𝑚∠1 = 180°;∠1 ≅ ∠2; 𝑚∠2 ≅ 𝑚∠3
Prove: ∠3 is a straight angle.
4. Given 8.5s - 81.7 = -9.23s + 148.79
Prove: s = 13

Click here to see answer by CPhill(1959) About Me 

Question 1184157: Construct two examples of bijective function from ZxZ to Q where Z is set of all integers and Q is set of rational numbers?
Click here to see answer by ikleyn(52778) About Me 
Question 1184157: Construct two examples of bijective function from ZxZ to Q where Z is set of all integers and Q is set of rational numbers?
Click here to see answer by CPhill(1959) About Me 

Question 1182545: In the 1992 presidential election, Alaska's 40 election districts averaged 2150 votes per district for President Clinton.
The standard deviation was 593.
(There are only 40 election districts in Alaska).
The distribution of the votes per district for President Clinton was bell-shaped.
Let X = number of votes for President Clinton for an election district.
Round all answers except part e. to 4 decimals.
a. What is the distribution of X?
X - N = 2150,593
b. Is 2150 a population mean or sample mean? Mean
c. Find the probability that a randomly selected district had fewer than 2142 votes for President Clinton.
d. Find the probability that a randomly selected district had between 2291 and 2561 votes for President Clinton.
e. Find the third quartile for votes President Clinton.
Round to the nearest whole number

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Question 1209234: Fill in the blank with a constant, so that the resulting expression can be
factored as the product of two linear expressions:
2ab - a + b + ___

Click here to see answer by greenestamps(13200) About Me 
Question 1209234: Fill in the blank with a constant, so that the resulting expression can be
factored as the product of two linear expressions:
2ab - a + b + ___

Click here to see answer by ikleyn(52778) About Me 
Question 1209234: Fill in the blank with a constant, so that the resulting expression can be
factored as the product of two linear expressions:
2ab - a + b + ___

Click here to see answer by Edwin McCravy(20054) About Me 

Question 1209235: Find the number of ordered pairs (m,n) of integers that satisfy
mn = 3m + 3n + 17.

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Question 1209235: Find the number of ordered pairs (m,n) of integers that satisfy
mn = 3m + 3n + 17.

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Question 1209235: Find the number of ordered pairs (m,n) of integers that satisfy
mn = 3m + 3n + 17.

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Question 1209235: Find the number of ordered pairs (m,n) of integers that satisfy
mn = 3m + 3n + 17.

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Question 1208689: Fill in the blanks with positive integers:
(3 + sqrt(6))^3 = ___ + ___ * sqrt(6)

Click here to see answer by math_tutor2020(3816) About Me 
Question 1208689: Fill in the blanks with positive integers:
(3 + sqrt(6))^3 = ___ + ___ * sqrt(6)

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Question 1208682: Fill in the blanks with positive integers:

(3 + sqrt(6))*3 = ___ + ___ * sqrt(6)

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Question 1208683: Expand (sqrt(x) + 3x)*4 + (sqrt(x) - 3x)*4.
Click here to see answer by greenestamps(13200) About Me 

Question 1207639: 75+72+69+66+.....21+18+15
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Question 1207639: 75+72+69+66+.....21+18+15
Click here to see answer by MathLover1(20849) About Me 

Question 1206996: To expand its business, Kingston Outlet Factory would like to issue a bond with par value of
₱1,000, coupon rate 10%, and maturity of 10 years. Calculate the bond amount given each of the
required rate of return.
a. 85%? b. 10%? c. 12%

Click here to see answer by Theo(13342) About Me 

Question 1206748: graph the inequalities of -24x+6y>18

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Question 1204582: -6a+7(-2a-4)

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Question 1204582: -6a+7(-2a-4)

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Question 1204292: Consider the binary operation defined by x * y=xy-2x-15 Solve x *2=0
Click here to see answer by ikleyn(52778) About Me 
Question 1204292: Consider the binary operation defined by x * y=xy-2x-15 Solve x *2=0
Click here to see answer by josgarithmetic(39617) About Me 

Question 1098110: Use the Commutative Property of Multiplication and the Associative Property of Multiplication to show the Power of a Product Property (a * b)^n = a^n * b^n is true.
Click here to see answer by math_tutor2020(3816) About Me 
Question 1098110: Use the Commutative Property of Multiplication and the Associative Property of Multiplication to show the Power of a Product Property (a * b)^n = a^n * b^n is true.
Click here to see answer by ikleyn(52778) About Me 

Question 1201311: 3v^2 -33v+27
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Question 1200518: 8-3z=2z+9
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Question 1200518: 8-3z=2z+9
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Question 1091106: Is the following true false or open?
6-t=12

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Question 1091106: Is the following true false or open?
6-t=12

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Question 1091106: Is the following true false or open?
6-t=12

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Question 1091106: Is the following true false or open?
6-t=12

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Question 1200110: +sqrt%283a%29%28sqrt%2812a%29+-+2sqrt%288a%5E2%29%29+
Does the +sqrt%283a%29+ distribute to the +2+ factor in the 2nd term or to just the
+sqrt%288a%5E2%29+ factor?
Either
+-6a%28sqrt%2824a%5E3%29%29+
or
+-2%28sqrt%2824a%5E3%29%29+ ???
Can you please give a complete explanation of this?
Thank you
jadams

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Question 1200110: +sqrt%283a%29%28sqrt%2812a%29+-+2sqrt%288a%5E2%29%29+
Does the +sqrt%283a%29+ distribute to the +2+ factor in the 2nd term or to just the
+sqrt%288a%5E2%29+ factor?
Either
+-6a%28sqrt%2824a%5E3%29%29+
or
+-2%28sqrt%2824a%5E3%29%29+ ???
Can you please give a complete explanation of this?
Thank you
jadams

Click here to see answer by josgarithmetic(39617) About Me 

Question 1200234: what is 4m=z but to determine how many ounces of water z he will need for the number of miles he hikes,if he hikes 20 miles, how many ounces of water will he need
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Question 1199995: Please help me understand ... If represents a random variable coming from a normal distribution and P(X<5)=0.47, then P(X>5)=0.53. True or False. Step by step please, thank you so much.


Click here to see answer by Theo(13342) About Me 

Question 1199838: why does 10b-b=9b

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Question 1199794: can u help me on this hehe i need 3 examples of every law of exponents(FIRST TO FOURTH LAW) thank you so much

The Product rule for radicals

root(xy, n) = root(x, n) * root(y, n)
where x and y are nonnegative numbers and n is a counting number.

The Quotient Rule for Radicals:
root(x/y, n) = (root(x, n)/(root(y, n)
where x and y are nonnegative numbers and y=0.
Additional Rule:
root(m) root(n) x = root(mn)x
Laws of Radicals
First Law of Exponents: xm. xn = xm+n
Second Law of Exponents: xm/xn = xm-n; if x = 0 and m>n
Third Law of Exponents: (xm)n = xmn
Fourth Law of Exponents: (xy)m = xmym
Extension of the Second Law of Exponents:
1. The Zero Exponent: x0 = 1; where x = 0.
2. Definition of Negative Exponent: x-n= 1/xn where x = 0 and n is a counting number.

Click here to see answer by josgarithmetic(39617) About Me 

Question 1199783: Phyllis invested $13,500, a portion earning a simple interest rate of 5 1/5% per year and the rest earning a rate of 5% per year. After 1 year the total interest earned on these investments was $692. How much money did she invest at each rate?
Click here to see answer by ikleyn(52778) About Me 

Question 1198732: Expand (2x+7y)^5.
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Question 1197372: Use the distributive property to expand: x^-3y^0(x^2-3x^5y^4)
Click here to see answer by ikleyn(52778) About Me 

Question 1196938: A rectangle has a width of 4 cm and a length of 10 cm. The rectangle is folded so that it creates a rectangle with a width of 4 cm and a length of 5 cm. The other rectangle has a width of 4 cm and a length of 5 cm. Write two expressions to show the area of the rectangle.
I got (4 x 5) + (4 x 5) and (4 x 5) x 2.
I am not sure if the expressions I got are correct, but I think they are because the rectangle has to have an area of 40 cm. Can you please help me with this question?

Click here to see answer by math_tutor2020(3816) About Me